> > > Whether or not something like d is in the rationals-complete list can only be judged by means of the d_n - at least in mathematics.> > > How can we judged the properties of a given object based the properties of a set of others object which the given object is not a member of?> > > Its like saying are cats are feline, hence my dog is a feline.> > No unsuitable analogies please. The difference of d and all entries of the list, if existing, does not fall down from heaven. It can be proven by digits which belong to FIS as well as to d or it cannot be proven.>

My analogy is not unsuitable. As you said that logic doesn't need context. So just take away context and realize something for once.

> > > > > What is the reason for this strange behaviour?> > > > > Because d is not one of the d_n, it can have properties that none of > > > > them can have, like not being one of them.> > > > The property of differing or not depends on the d_n only. Note that Cantor's diagonal argument only uses the d_n.>

No, it use the enire complete diagonal.

> > The property of differing depends on All place values of the decimal representation of d.> > That is easy to contradict. The property does not depend on the first n digits. They have many duplicates. For every n in |N.>